1. Линейные уравнения.

Решение:

Ниже приведены решения линейных уравнений:

1. \( 6x + 18 = 0 \)
   \( 6x = -18 \)
   \( x = -3 \)
2. \( 5x - 3 = 0 \)
   \( 5x = 3 \)
   \( x = \frac{3}{5} \)
3. \( 27 - 9x = 0 \)
   \( 27 = 9x \)
   \( x = 3 \)
4. \( -2x - 3 = 1 \)
   \( -2x = 4 \)
   \( x = -2 \)
5. \( -4x + 4 = -6 \)
   \( -4x = -10 \)
   \( x = \frac{-10}{-4} = \frac{5}{2} \)
6. \( -5x + 8 = -2 \)
   \( -5x = -10 \)
   \( x = 2 \)
7. \( 8x - 5 = 10x \)
   \( -5 = 2x \)
   \( x = -\frac{5}{2} \)
8. \( 6x = x - 2 \)
   \( 5x = -2 \)
   \( x = -\frac{2}{5} \)
9. \( 4x + 5 = -4x \)
   \( 8x = -5 \)
   \( x = -\frac{5}{8} \)
10. \( 6 + 3x = 4x - 1 \)
    \( 7 = x \)
11. \( 1 + 2x = 10x + 3 \)
    \( -2 = 8x \)
    \( x = -\frac{2}{8} = -\frac{1}{4} \)
12. \( 6x + 4 = 5x - 18 \)
    \( x = -22 \)
13. \( 2(x - 7) = 3 \)
    \( 2x - 14 = 3 \)
    \( 2x = 17 \)
    \( x = \frac{17}{2} \)
14. \( 3 = 4(x + 2) \)
    \( 3 = 4x + 8 \)
    \( -5 = 4x \)
    \( x = -\frac{5}{4} \)
15. \( 3(x - 4) = 6 \)
    \( 3x - 12 = 6 \)
    \( 3x = 18 \)
    \( x = 6 \)
16. \( 2(7 + 9x) = -6x + 2 \)
    \( 14 + 18x = -6x + 2 \)
    \( 24x = -12 \)
    \( x = -\frac{12}{24} = -\frac{1}{2} \)
17. \( 9 + 2(2x + 1) = 1 \)
    \( 9 + 4x + 2 = 1 \)
    \( 4x + 11 = 1 \)
    \( 4x = -10 \)
    \( x = -\frac{10}{4} = -\frac{5}{2} \)
18. \( -7 + 2(7x - 2) = 10 \)
    \( -7 + 14x - 4 = 10 \)
    \( 14x - 11 = 10 \)
    \( 14x = 21 \)
    \( x = \frac{21}{14} = \frac{3}{2} \)
19. \( -3x + 4 = -10 + 5(-7 - x) \)
    \( -3x + 4 = -10 - 35 - 5x \)
    \( -3x + 4 = -45 - 5x \)
    \( 2x = -49 \)
    \( x = -\frac{49}{2} \)
20. \( 6x - 8(-7 + 9x) = -2x - 8 \)
    \( 6x + 56 - 72x = -2x - 8 \)
    \( -66x + 56 = -2x - 8 \)
    \( -64x = -64 \)
    \( x = 1 \)
21. \( (x + 3)² = (x + 8)² \)
    \( x^2 + 6x + 9 = x^2 + 16x + 64 \)
    \( 6x + 9 = 16x + 64 \)
    \( -55 = 10x \)
    \( x = -5.5 \)
22. \( (x - 5)² = (x - 8)² \)
    \( x^2 - 10x + 25 = x^2 - 16x + 64 \)
    \( -10x + 25 = -16x + 64 \)
    \( 6x = 39 \)
    \( x = \frac{39}{6} = \frac{13}{2} \)
23. \( (x + 1)² = (2 - x)² \)
    \( x^2 + 2x + 1 = 4 - 4x + x^2 \)
    \( 2x + 1 = 4 - 4x \)
    \( 6x = 3 \)
    \( x = \frac{1}{2} \)